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106
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COMBINATORICS
2006
112views more  COMBINATORICS 2006»
15 years 3 months ago
More Forbidden Minors for Wye-Delta-Wye Reducibility
A graph is Y Y reducible if it can be reduced to isolated vertices by a sequence of series-parallel reductions and Y Y transformations. It is still an open problem to characterize...
Yaming Yu
COMBINATORICS
2006
103views more  COMBINATORICS 2006»
15 years 3 months ago
A Note on Domino Shuffling
We present a variation of James Propp's generalized domino shuffling, which provides an efficient way to obtain perfect matchings of weighted Aztec diamonds. Our modification...
É. Janvresse, T. de la Rue, Y. Velenik
115
Voted
COMBINATORICS
2006
132views more  COMBINATORICS 2006»
15 years 3 months ago
On Computing the Distinguishing Numbers of Trees and Forests
Let G be a graph. A vertex labeling of G is distinguishing if the only label-preserving automorphism of G is the identity map. The distinguishing number of G, D(G), is the minimum...
Christine T. Cheng
118
Voted
COMBINATORICS
2006
155views more  COMBINATORICS 2006»
15 years 3 months ago
Orthogonal Art Galleries with Holes: A Coloring Proof of Aggarwal's Theorem
We prove that n+h 4 vertex guards are always sufficient to see the entire interior of an n-vertex orthogonal polygon P with an arbitrary number h of holes provided that there exis...
Pawel Zylinski
COMBINATORICS
2006
131views more  COMBINATORICS 2006»
15 years 3 months ago
Encores on Cores
We give a new derivation of the threshold of appearance of the k-core of a random graph. Our method uses a hybrid model obtained from a simple model of random graphs based on rand...
Julie Cain, Nicholas C. Wormald